Trac #32215: Asymptotic Term Monoids: refactor element construction

In #31933 conversion fails. In order to fix this properly, a refactor of
the conversion process seems the best solution. This ticket does this
(without fixing the open issue on #31933 which will be a follow up).

URL: https://trac.sagemath.org/32215
Reported by: dkrenn
Ticket author(s): Daniel Krenn
Reviewer(s): Benjamin Hackl

Author: Release Manager

build/pkgs/configure/checksums.ini

@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
-sha1=766d040ff9b94c355e1e340ba2b4a7bc2fbc4a2f
-md5=154dee70c098f55a683291398591fee2
-cksum=1315912721
+sha1=fa7a6a287c18e8c4129ef5e7f098e716bd30f73f
+md5=a342ed4d433163a2dbb43f2202740575
+cksum=2901964880

build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-42052ec4ff3edacd2c8d8df6a73ad5e63731d0f7
+1ed7c6033bc77e3dffbd60b0777d3b939a4226b4

src/sage/rings/asymptotic/asymptotic_ring.py

@@ -575,7 +575,7 @@ def __init__(self, parent, summands, simplify=True, convert=True):
             sage: G = GrowthGroup('x^ZZ'); x = G.gen()
             sage: OT = TermMonoid('O', G, ZZ); ET = TermMonoid('exact', G, ZZ)
             sage: R = AsymptoticRing(G, ZZ)
-            sage: lst = [ET(x, 1), ET(x^2, 2), OT(x^3), ET(x^4, 4)]
+            sage: lst = [ET(x, coefficient=1), ET(x^2, coefficient=2), OT(x^3), ET(x^4, coefficient=4)]
             sage: expr = R(lst, simplify=False); expr  # indirect doctest
             4*x^4 + O(x^3) + 2*x^2 + x
             sage: print(expr.summands.repr_full())
@@ -641,8 +641,10 @@ def __init__(self, parent, summands, simplify=True, convert=True):
             ValueError: Cannot include 1/2 with parent
             Exact Term Monoid x^QQ with coefficients in Rational Field in
             Asymptotic Ring <x^QQ> over Integer Ring
-            > *previous* ValueError: 1/2 is not a coefficient in
-            Exact Term Monoid x^QQ with coefficients in Integer Ring.
+            > *previous* ValueError: Cannot create ExactTerm(1)
+              since given coefficient 1/2 is not valid in
+              Exact Term Monoid x^QQ with coefficients in Integer Ring.
+            >> *previous* TypeError: no conversion of this rational to integer
 
         Check :trac:`19921`::
 
@@ -949,7 +951,7 @@ def _simplify_(self):
             sage: G = GrowthGroup('x^ZZ')
             sage: OT = TermMonoid('O', G, ZZ); ET = TermMonoid('exact', G, ZZ)
             sage: R = AsymptoticRing(G, ZZ)
-            sage: lst = [ET(x, 1), ET(x^2, 2), OT(x^3), ET(x^4, 4)]
+            sage: lst = [ET(x, coefficient=1), ET(x^2, coefficient=2), OT(x^3), ET(x^4, coefficient=4)]
             sage: expr = R(lst, simplify=False); expr  # indirect doctest
             4*x^4 + O(x^3) + 2*x^2 + x
             sage: expr._simplify_(); expr
@@ -1079,7 +1081,9 @@ def monomial_coefficient(self, monomial):
             ValueError: Cannot include n with parent Exact Term Monoid
             n^QQ with coefficients in Rational Field in Asymptotic Ring
             <m^QQ> over Rational Field
-            > *previous* ValueError: n is not in Growth Group m^QQ.
+            > *previous* ValueError: Growth n is not valid in
+              Exact Term Monoid m^QQ with coefficients in Rational Field.
+            >> *previous* ValueError: n is not in Growth Group m^QQ.
 
         Only monomials are allowed::
 
@@ -3068,8 +3072,10 @@ def map_coefficients(self, f, new_coefficient_ring=None):
             sage: a.map_coefficients(lambda c: 1/c)
             Traceback (most recent call last):
             ...
-            ValueError: ... is not a coefficient in
+            ValueError: Cannot create ExactTerm(n^3) since
+            given coefficient 1/2 is not valid in
             Exact Term Monoid n^ZZ with coefficients in Integer Ring.
+            > *previous* TypeError: no conversion of this rational to integer
         """
         def mapping(term):
             T = term.parent().change_parameter(
@@ -3078,7 +3084,7 @@ def mapping(term):
                 c = f(term.coefficient)
                 if c.is_zero():
                     return None
-                return T(term.growth, c)
+                return T(term.growth, coefficient=c)
             else:
                 return T(term.growth)
 
@@ -3922,7 +3928,7 @@ def _element_constructor_(self, data, simplify=True, convert=True):
             ...
             ValueError: Polynomial y is not in
             Asymptotic Ring <x^ZZ> over Integer Ring
-            > *previous* ValueError: Growth y is not in
+            > *previous* ValueError: Growth y is not valid in
             Exact Term Monoid x^ZZ with coefficients in Integer Ring.
             >> *previous* ValueError: y is not in Growth Group x^ZZ.
 
@@ -3965,7 +3971,7 @@ def _element_constructor_(self, data, simplify=True, convert=True):
             ...
             ValueError: Polynomial a + c is not in
             Asymptotic Ring <a^ZZ * b^ZZ> over Rational Field
-            > *previous* ValueError: Growth c is not in
+            > *previous* ValueError: Growth c is not valid in
             Exact Term Monoid a^ZZ * b^ZZ with coefficients in Rational Field.
             >> *previous* ValueError: c is not in Growth Group a^ZZ * b^ZZ.
             >...> *previous* ValueError: c is not in any of the factors
@@ -3983,7 +3989,9 @@ def _element_constructor_(self, data, simplify=True, convert=True):
             ValueError: Cannot include m^3 with parent
             Exact Term Monoid m^ZZ with coefficients in Integer Ring
             in Asymptotic Ring <n^ZZ> over Rational Field
-            > *previous* ValueError: m^3 is not in Growth Group n^ZZ.
+            > *previous* ValueError: Growth m^3 is not valid in
+              Exact Term Monoid n^ZZ with coefficients in Rational Field.
+            >> *previous* ValueError: m^3 is not in Growth Group n^ZZ.
 
         ::
 
@@ -4539,7 +4547,7 @@ def create_summand(self, type, data=None, **kwds):
             sage: R.create_summand('O', growth=42*x^2, coefficient=1)
             Traceback (most recent call last):
             ...
-            ValueError: Growth 42*x^2 is not in O-Term Monoid x^ZZ with implicit coefficients in Integer Ring.
+            ValueError: Growth 42*x^2 is not valid in O-Term Monoid x^ZZ with implicit coefficients in Integer Ring.
             > *previous* ValueError: 42*x^2 is not in Growth Group x^ZZ.
 
         ::